Given the Fourier series
$$f(z) = \sum_{k=-\infty}^\infty c_k e^{ikz}$$
but with $c_k\in(\mathbb Q+ i\mathbb Q)$ instead of $\mathbb C$ (or even purely real), are the functions obtained this way in ...

There is an exercise in my text that tells me to prove the "obvious and easy to see" fact that $\mathbb{Z}$ and $\mathbb{Q}$ have measure zero.
Er...here is what I know so far. If I have an interval, ...

If $a \in \mathbb{I}$ , how is $$\overline{\mathbb{Z}+ a\mathbb{Z}}=\mathbb{R}$$
It says in my notebook that this set in dense in $\mathbb{R}.$ How do I prove this density? With say $\mathbb{Q}$ and ...

I'm looking for a clear, thorough, and easy-to-follow introduction to Dedekind cuts that is specifically geared towards those with an interest in foundational issues. So far, the discussions that I ...

What is a proof that $\ln(\alpha)$ is transcendental for $\alpha$. I believe I heard somewhere that the natural logarithm of any rational number is transcendental. Do you guys have any proofs of that ...

Prove that rational numbers (not just positive) are countable without using axiom of choice(since it is controversial).
I have seen proofs that use the fact that union of countable sets is countable, ...

Suppose I have been given a rational number in decimal format (since decimals of rationals repeat, finite precision presentation suffices), what is the most effective way to write it in form of ratio ...

I would like an alternate solution and proof verification for the following problem:
Find all continuous functions $f:\mathbb R \rightarrow \mathbb R$ so that if $x-y$ is rational then $f(x)-f(y)$ is ...

Upon dividing two integers, I would like to programmatically predict the number of decimal places that repeat after the decimal point.
For example in $\frac{1}{3}=0.\overline{3}$, I want to know that ...

The answer is not "200 questions", though it would be if he got a score of exactly 38.5%. The fact that anything that rounds to the nearest decimal is allowed complicates things.
I know the answer, ...

Why do we switch the denominator and numerator when we divide fractions?
I've been trying to find out why and I've asked several people and checked many websites but none that give me a good answer. ...

As an exercise in my conceptual algebra class we attempted to determine the reason why this theorem holds true in the forward direction. (Note we decided not to tackle the opposite direction) I wrote ...

Consider a function $f$ from the positive rationals to the reals such that $f(x)f(y)\ge f(xy)$ and $f(x+y)\ge f(x)+f(y)$. Further assume this function has a fixed point greater than $1$. Prove this ...

About one hour ago I asked a question which at first sight looked non-trivial to me but it is really trivial. Shame on me, whether I want it or not.
Now I have, solely for fun, another question which ...

I was reading some question on this site and stream of thought led me to the creation of another question that could be trivial for someone but I am unable even to start solving it. I wanna share this ...

I'm in confusion from some time about division of negative numbers. When we divide a positive number with a positive number, for example $$5/3 = 1.66 $$
we see what is biggest multiple of 3 which is ...

Hi this might seem like a really stupid question but then hopefully someone can asnswer it quite easily :)
I have function $P{_t}$$=(E{_t}$ $(P{_t}{_+}{_1}+$ $δ{_t}{_+}{_1}$$ )-γΩx$${^*})/$$(1+rf+ψ_t ...

I've tried to look for similar things on StackExchange and elsewhere on the net, but can't seem to find anything, so thought I'd just ask for some help on here...
Someone has kindly helped me with a ...

When I was comparing proof for $\sqrt{2}$ and sum of two rational numbers, I found that the proof of two rational number did not mention anything about common factor in the ratio.
one proof I found ...

We know that $\mathbb{Q}\cong\mathbb{Z}\times\mathbb{Z}/\sim$, where the isomorphism is a ring isomorphism and the equivalence relation is defined as
$$(a,b)\sim(c,d)\Longleftrightarrow ad=bc$$
Then ...

I'm looking for a proof to show when $p^q$ for $p,q \in \mathbb{Q}$ is again in $\mathbb{Q}$, without factoring. I'm not sure, if it's possible, given these two numbers to say if the result is again ...

Given any interval $I=(a,b) \subset \mathbb R^+$, we may order the rationals in $I$ with a denominator-first lexicographic order, as follows: First, we list, in increasing order of numerator, all $q ...